Rule: Q[2, 80, 83]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{82}-41\cdot t^{80}+\frac{3239}{8}\cdot t^{78}-\frac{41041}{16}\cdot t^{76}+\frac{1499575}{128}\cdot t^{74}-\frac{10520395}{256}\cdot t^{72}+\frac{117939165}{1024}\cdot t^{70}-\frac{542520159}{2048}\cdot t^{68}+\frac{16700823273}{32768}\cdot t^{66}-\frac{54525518905}{65536}\cdot t^{64}+\frac{76335726467}{65536}\cdot t^{62}-\frac{184828244237}{131072}\cdot t^{60}+\frac{1557838058569}{1048576}\cdot t^{58}-\frac{2870798562781}{2097152}\cdot t^{56}+\frac{9287877703115}{8388608}\cdot t^{54}-\frac{13224828848913}{16777216}\cdot t^{52}+\frac{265698834146343}{536870912}\cdot t^{50}-\frac{294553006180335}{1073741824}\cdot t^{48}+\frac{4614663763491915}{34359738368}\cdot t^{46}-\frac{3990122803019325}{68719476736}\cdot t^{44}+\frac{12176310231149295}{549755813888}\cdot t^{42}-\frac{8184077368477395}{1099511627776}\cdot t^{40}+\frac{9672091435473285}{4398046511104}\cdot t^{38}-\frac{5010670802607015}{8796093022208}\cdot t^{36}+\frac{18142083940473675}{140737488355328}\cdot t^{34}-\frac{7142251993407531}{281474976710656}\cdot t^{32}+\frac{2433074854897071}{562949953421312}\cdot t^{30}-\frac{712718896889041}{1125899906842624}\cdot t^{28}+\frac{712718896889041}{9007199254740992}\cdot t^{26}-\frac{150705036752725}{18014398509481984}\cdot t^{24}+\frac{53326397620195}{72057594037927936}\cdot t^{22}-\frac{7791522991945}{144115188075855872}\cdot t^{20}+\frac{29607787369391}{9223372036854775808}\cdot t^{18}-\frac{2801478953319}{18446744073709551616}\cdot t^{16}+\frac{823964398035}{147573952589676412928}\cdot t^{14}-\frac{45581009253}{295147905179352825856}\cdot t^{12}+\frac{7266537707}{2361183241434822606848}\cdot t^{10}-\frac{196392911}{4722366482869645213696}\cdot t^8+\frac{6577753}{18889465931478580854784}\cdot t^6-\frac{58835}{37778931862957161709568}\cdot t^4+\frac{1681}{604462909807314587353088}\cdot t^2-\frac{1}{1208925819614629174706176}$
• $P_3$:
  $2\cdot t^{165}-83\cdot t^{163}+1691\cdot t^{161}-22545\cdot t^{159}+\frac{28316681}{128}\cdot t^{157}-\frac{436151495}{256}\cdot t^{155}+\frac{5490594109}{512}\cdot t^{153}-\frac{58089087771}{1024}\cdot t^{151}+\frac{8433465020475}{32768}\cdot t^{149}-\frac{66652694313865}{65536}\cdot t^{147}+\frac{116103435630455}{32768}\cdot t^{145}-\frac{1440321110095735}{131072}\cdot t^{143}+\frac{128267530921381215}{4194304}\cdot t^{141}-\frac{644883788715016025}{8388608}\cdot t^{139}+\frac{2945058495080912357}{16777216}\cdot t^{137}-\frac{12274780777391634943}{33554432}\cdot t^{135}+\frac{1500232123731579692769}{2147483648}\cdot t^{133}-\frac{5269332976556936044131}{4294967296}\cdot t^{131}+\frac{8535968399886948290985}{4294967296}\cdot t^{129}-\frac{3197265858740620160637}{1073741824}\cdot t^{127}+\frac{284215897395897838584213}{68719476736}\cdot t^{125}-\frac{733436618251947293666475}{137438953472}\cdot t^{123}+\frac{1761385272260348799417525}{274877906944}\cdot t^{121}-\frac{3942864756011080396228875}{549755813888}\cdot t^{119}+\frac{131813352061572292852993725}{17592186044416}\cdot t^{117}-\frac{257386813912668677357403855}{35184372088832}\cdot t^{115}+\frac{29386943211229138140456015}{4398046511104}\cdot t^{113}-\frac{402155838579852628772047855}{70368744177664}\cdot t^{111}+\frac{10315040214824363347957397825}{2251799813685248}\cdot t^{109}-\frac{15506980846257736041275354615}{4503599627370496}\cdot t^{107}+\frac{21874023577362113304228786375}{9007199254740992}\cdot t^{105}-\frac{28965152050711527465906033085}{18014398509481984}\cdot t^{103}+\frac{2305192003408544909837207335735}{2305843009213693952}\cdot t^{101}-\frac{2692657223428169219315080827125}{4611686018427387904}\cdot t^{99}+\frac{1477501404331784302356984985425}{4611686018427387904}\cdot t^{97}-\frac{761764874166282566725744731825}{4611686018427387904}\cdot t^{95}+\frac{188946006840307861783576202590325}{2361183241434822606848}\cdot t^{93}-\frac{172004919291290640730220823991675}{4722366482869645213696}\cdot t^{91}+\frac{147098567795461258769253704868625}{9444732965739290427392}\cdot t^{89}-\frac{118152881375500340859028374406263}{18889465931478580854784}\cdot t^{87}+\frac{1425732793249340419735595117256227}{604462909807314587353088}\cdot t^{85}-\frac{1009218474181506206459496364709153}{1208925819614629174706176}\cdot t^{83}+\frac{167550539733172478187786662543593}{604462909807314587353088}\cdot t^{81}-\frac{208657889998088376195516566128995}{2417851639229258349412352}\cdot t^{79}+\frac{1947961493381575373652608433648327}{77371252455336267181195264}\cdot t^{77}-\frac{1064297420863342895990794378503249}{154742504910672534362390528}\cdot t^{75}+\frac{544068962287673151074451062252805}{309485009821345068724781056}\cdot t^{73}-\frac{259994034392851557111702311222895}{618970019642690137449562112}\cdot t^{71}+\frac{3712857798639493820679777617523075}{39614081257132168796771975168}\cdot t^{69}-\frac{1545646552262523773815299120007785}{79228162514264337593543950336}\cdot t^{67}+\frac{299751844536670141742360224048047}{79228162514264337593543950336}\cdot t^{65}-\frac{27044837069501026927168432499799}{39614081257132168796771975168}\cdot t^{63}+\frac{290190374806231404457934397015897}{2535301200456458802993406410752}\cdot t^{61}-\frac{90261598634826822591905298438855}{5070602400912917605986812821504}\cdot t^{59}+\frac{25997665979627678843744143430481}{10141204801825835211973625643008}\cdot t^{57}-\frac{6920633182303037531541520613055}{20282409603651670423947251286016}\cdot t^{55}+\frac{27186184110306451224487011294549}{649037107316853453566312041152512}\cdot t^{53}-\frac{6141954639230282476402161906231}{1298074214633706907132624082305024}\cdot t^{51}+\frac{159206468141122596829639445025}{324518553658426726783156020576256}\cdot t^{49}-\frac{120880005848089194518656232115}{2596148429267413814265248164610048}\cdot t^{47}+\frac{335029708025109233249348496345}{83076749736557242056487941267521536}\cdot t^{45}-\frac{52786055607284930371015885695}{166153499473114484112975882535043072}\cdot t^{43}+\frac{7536728223647193862457421255}{332306998946228968225951765070086144}\cdot t^{41}-\frac{971186275221425121962258925}{664613997892457936451903530140172288}\cdot t^{39}+\frac{14391911839547928451810707663}{170141183460469231731687303715884105728}\cdot t^{37}-\frac{1489401941179385885474705757}{340282366920938463463374607431768211456}\cdot t^{35}+\frac{68500953954831444629280669}{340282366920938463463374607431768211456}\cdot t^{33}-\frac{2782414015712510036367603}{340282366920938463463374607431768211456}\cdot t^{31}+\frac{12683592305984333023810365}{43556142965880123323311949751266331066368}\cdot t^{29}-\frac{785531037711792567562899}{87112285931760246646623899502532662132736}\cdot t^{27}+\frac{41899834537508397147633}{174224571863520493293247799005065324265472}\cdot t^{25}-\frac{1903531195938647086695}{348449143727040986586495598010130648530944}\cdot t^{23}+\frac{1163182633613052965055}{11150372599265311570767859136324180752990208}\cdot t^{21}-\frac{36768056998146801525}{22300745198530623141535718272648361505980416}\cdot t^{19}+\frac{235993638505585455}{11150372599265311570767859136324180752990208}\cdot t^{17}-\frac{9615805137200691}{44601490397061246283071436545296723011960832}\cdot t^{15}+\frac{2415273922674963}{1427247692705959881058285969449495136382746624}\cdot t^{13}-\frac{28120221427077}{2854495385411919762116571938898990272765493248}\cdot t^{11}+\frac{230545201905}{5708990770823839524233143877797980545530986496}\cdot t^9-\frac{1235891331}{11417981541647679048466287755595961091061972992}\cdot t^7+\frac{123579945}{730750818665451459101842416358141509827966271488}\cdot t^5-\frac{183803}{1461501637330902918203684832716283019655932542976}\cdot t^3+\frac{41}{1461501637330902918203684832716283019655932542976}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.